Factor the following equations:

1. $ 7p^2 - 7p = 7p(p - 1) $

2. $ 18xy + 3y = 3y(6x + 1) $

3. $ 15t^3 - 15t^2 + 20t = 5t(3t^2 - 3t + 4) $

4. $ 17x^5 - 51x^4 - 34x = 17x(x^4 - 3x^3 - 2) $

5. $ 35x^5y^2 + 21x^4y + 14x^3y^2 = 7x^3y^2(5x^2 + 3xy + 2) $

The provided equations are each rewritten in factored form as follows: 7ₚ² - 7ₚ = 7ₚ(ₚ - 1), 18ₓᵧ + 3ᵧ = 3ᵧ(6ₓ + 1), 15ₜ³ - 15ₜ² + 20ₜ = 5ₜ(3ₜ² - 3ₜ + 4), 17ₓ⁵ - 51ₓ⁴ - 34ₓ = 17ₓ(ₓ⁴ - 3ₓ³ - 2), 35ₓ⁵ᵧ² + 21ₓ⁴ᵧ + 14ₓ³ᵧ² = 7ₓ³ᵧ²(5ₓ² + 3ₓᵧ + 2).

Explanation:

The given equations are factored to express the left-hand side as a product of two expressions. This factoring simplifies the equations and reveals common factors that help in solving or understanding the behavior of the expressions.

In the first equation, factoring out 7ₚ from 7ₚ² - 7ₚ yields 7ₚ(ₚ - 1). Similarly, the other equations are factored using distributive properties to express them as a product of their common factors.

These factored forms highlight the mathematical relationships between the terms and provide a clearer representation of the equations.

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Complete Question;

Equations: 7p² - 7p = 7p(p - 1) 18xy + 3y = 3y(6x + 1) 15t³ - 15t² + 20t = 5t(3t² - 3t + 4) 17x⁵ - 51x⁴ - 34x = 17x(x⁴ - 3x³ - 2) 35x⁵y² + 21x⁴y + 14x³y² = 7x³y²(5x² + 3xy + 2) rewriote in factored.

Factor the following equations:1. \( 7p^2 - 7p = 7p(p - 1) \)2. \( 18xy + 3y = 3y(6x + 1) \)3. \( 15t^3 - 15t^2 + 20t = 5t(3t^2 - 3t + 4) \)4. \( 17x^5 - 51x^4 - 34x = 17x(x^4 - 3x^3 - 2) \)5. \( 35x^5y^2 + 21x^4y + 14x^3y^2 = 7x^3y^2(5x^2 + 3xy + 2) \)

Answer :

Other Questions

Factor the following equations:

1. \( 7p^2 - 7p = 7p(p - 1) \)

2. \( 18xy + 3y = 3y(6x + 1) \)

3. \( 15t^3 - 15t^2 + 20t = 5t(3t^2 - 3t + 4) \)

4. \( 17x^5 - 51x^4 - 34x = 17x(x^4 - 3x^3 - 2) \)

5. \( 35x^5y^2 + 21x^4y + 14x^3y^2 = 7x^3y^2(5x^2 + 3xy + 2) \)